A Model of the Emergence of Early Imitation
Development based on Predictability Preference
Takashi Minato, Dale Thomas, Yuichiro Yoshikawa, and Hiroshi Ishiguro
Asada Project, ERATO, Japan Science and Technology Agency
Graduate School of Engineering, Osaka University, Suita, Osaka, 565-0871, Japan
Email:minato@jeap.org

Abstract—This article presents a mechanism for the early
development of imitation through a simulation of infant-caregiverinteraction. A model was created to acquire a body mapping(a mapping from observed body motions to motor commands),
which is necessary for imitation, while discriminating self-motion
from the motion of the other. The simulation results show thatthe development of a body mapping depends on a predictability
preference (a function of how an agent decides regarding its
options of ‘what to imitate’). The simulated infants are able
to develop the components of a healthy body mapping in order,that is, relating self motion first, followed by an understanding ofothers’ motions, which is supported by psychological studies. Thisorder of development emerges spontaneously without the needfor any explicit mechanism or any partitioning of the interaction.
These results suggest that this predictability preference is an
important factor in infant imitation development.

I. I NTRODUCTION
Imitation is a very important function in human infantdevelopment, especially for the development of our ability
to understand and communicate with others. For example,
simulation theory has suggested that the capacity to understandothers’ internal state relies on a process which matches theobserved behavior with the action of the observer, that is, imitation by the observer [1]. According to Piaget’s developmental
theory [2], infant’s imitative behaviors (shown in TABLE I)
are observed during the infants learn to coordinate their senses
and motor skills in the first two years. Before infants cometo imitate other persons in the stage 3, they show repetitive
behaviors (it seems they are mainly attentive to their bodies)in the stage 2. This process (from stage 2 to 3) also has been
observed in other studies [3]. It is, meanwhile, suggested that
infants develop a sense of self after birth [4], that is, selfknowledge of infants is formed in the developmental process.
Infants, therefore, may not distinguish self-produced motions
from motions produced by others on their perception in theearly developmental process. However, infants come to repeat
their own motions in advance of imitating others even though
they are frequently near other people (caregivers) and they may
observe not only self-produced motions but also movements
produced by others. In primary circular reactions, infants may
not recognize ’their body’ motions but just respond to interesting events, however, it is considered this reactions works
as self-imitation for development of infant’s sensorimotor
coordination [5]. We infer that the infant acquires the ability to
distinguish self from others during this process (the transition

TABLE II NFANT BEHAVIORS IN P IAGET ’ S STAGES OF COGNITIVE DEVELOPMENT.
Stage (Age)Stage 1
(0–1 month)Stage 2
(1–4 months)

Stage 3
(4–8 months)

Stage 4
(8–12 months)

Stage 5
(12–18 months)
Stage 6(18–24 months)

Infants’ behaviors
Infants operate based on reflexes.
Infants show primary circular reactions (reproductionof an interesting event initially occurred by chance)
involving their own bodies (e.g., repeating the motionof passing their hand before their face).
Infants actively experience the effects their behaviors
on external objects and repeat actions to bring about adesirable consequence (secondary circular reactions).
Infant imitates an adult who is imitating him/her.
Infants coordinate actions into new and more complex
sequences and start to show intentional, goal-directedbehaviors. Infants can imitate behaviors without feedback (e.g., facial gestures).
Infants experiment with new behavior in a purposeful,trial-and-error way (tertiary circular reactions). Infants
actively imitate new behaviors.
Infants develop the ability to use primitive symbols.
Infants become capable of deferred imitation and start
to solve certain types of problems mentally.

from self to mutual imitation). This developmental process is
considered to be essential for imitation development, however,not many studies have focused on this mechanism. This paper
focuses on the mechanism of the transition from self to mutual
imitation in the process of acquiring a body mapping.
A crucial problem in imitation is the correspondence problem, in which the imitator needs to translate a sensory representation of the observed behavior into his/her own motor
representation for that behavior. [6, 7]. In order to solve thisproblem, it is necessary to acquire a body mapping thatassociates an observed motion with the corresponding motor
commands needed to perform the same action. Although somestudies have suggested that infants have an innate body mapping [8], we consider a neonate’s body mapping to be not sufficiently innate and that it is acquired, at least in part, throughsensorimotor experiences after birth, as suggested by someother studies such as an associative sequence learning (ASL)
theory [9]. Self-imitation requires a mapping that associates anobserved self-motion with the corresponding motor command(hereafter called the ‘self-model’), while other-imitation needs
a mapping that associates an observed other-motion with thecorresponding motor command (hereafter called the ‘othermodel’). The development of imitation capabilities should
involve the acquisition of these two models, with whichself and other’s motions become distinguishable. This paper
accounts for it as the development of self-other distinction in
the body mapping acquisition.
Some studies have focused on the mechanisms of bodymapping acquisition. Oztop and Arbib [10] proposed a modelto acquire a body mapping related to grasping motions througha hand state which is a viewpoint-independent image feature.
An alternative clue, which aids the learning of the bodymapping, is when the learner is imitated by another person.
In fact, it has been reported that caregivers frequently imitate their baby in various situations [11, 12]. Yokoya et al.
[13] suggested that a body mapping is acquired through theprocess of being imitated by another person. However, thesestudies assumed that other persons (caregivers) can already bediscriminated from self and that the self-model is acquired first
and then followed by the acquisition of the other-model basedon the prior learned self-model. This explicit partitioning ofinteraction does not happen in real world situations; that is, at
no point do infants get an opportunity to fully develop theirself-model in the absence of any other environmental factors
and only then start to have caregivers interact with them.
ASL theory [9] also considers a body mapping acquisitionby other’s imitation, however, the developmental process ofthe transition from self to mutual imitation is not considered.
This paper reports a study of a mechanism behind thedevelopment of an infant’s body mapping which enables selfimitation and the ability to imitate others through infantcaregiver interaction. This mechanism concerns the acquisitionof imitation capabilities and the ability to distinguish selffrom others in the circumstance of being with a caregiver. We
study the mechanism through a computer simulation of infantcaregiver interaction in the standpoint of the constructivist
approach called Cognitive Developmental Robotics [14]. Since
the study on the mechanism of imitation development is
an intricate issue, imitation development was simplified into
the acquisition of self-model and other-model through infantcaregiver interaction and, in addition, essential factors forbringing about the transition from self to mutual imitation
were explored. We built a minimal model to represent the
body mapping and simulated interactions between infant andcaregiver. We focused only on the imitative behaviors of theinfant and the caregiver in their interaction and did not specify
their task explicitly. In order to learn the body mapping, infant
needs to be imitated by caregiver, and also infant needs toimitate caregiver because it is considered caregiver’s imitative
behavior is elicited when he/she is imitated [15]. At first the
infant cannot correctly imitate because of his/her immaturebody mapping and proceeds to learn the mapping through theimitative interaction. During this interaction, the infant andcaregiver need to choose a motion from one corresponding
to self motion (self-imitation) and one corresponding to theother’s motion (imitating other). This motion selection problem possibly relies on the predictability of the observation
since it has been observed that infants are highly sensitive tocontingency [16]. We propose a mechanism for the motion
decision that uses a predictability preference, which is theWavingleft hand

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preference for a motion modulated by the predictability. It
is expected that the infant does not acquire the body mapping
if the caregiver never imitates the infant because we assume
the body mapping is constructed owing to other’s imitation.
It is also expected that the infant is unable to discriminate
self from other if the infant and caregiver keep imitating eachother with same motion because the self motor command canbe matched with equally both of the observed self-motion andother’s motion. It is inferred that the motion selection affects
the course of the interaction and the development of imitation.
This paper shows that the predictability preference which istypical for healthy people can lead to the successful learningof body mapping. It is generally desired that a developmental
model can also reproduce disordered development when themodel has some deficits in order to show the validity of themodel. We also investigate imitation development when theinfant has an atypical predictability preference. The paper
suggests that the predictability preference is one of the mostimportant factors governing the development of body mapping,which involves the development of self-other distinction andimitation, by showing how a typical preference results in a
typical developmental process and atypical preferences leadto a disordered body mapping.
II. A MODEL FOR EARLY IMITATION DEVELOPMENT
In order to deal with the issue of the imitation development,
we built a minimal model to represent the body mapping andthe infant-caregiver interaction. To simplify the model, we
make the following assumptions:• Body motions are spatially and temporally discretized.
A body motion is a gestural motion pattern such as
waving a right hand from side to side and moving a left
forearm up and down. A body motion is performed in
one time step.
• The infant and caregiver have homologous body motions.
• The agent shows motion either by trying to imitate, orby selecting an action to be performed randomly (here,“agent” denotes infant or caregiver). Also, no explicit task
is given to either agent.
An example of infant-caregiver interaction is shown in
Fig.1, in which both agents perform a body motion at
the same time and observe both their own motion andthat of the other. The caregiver in time step t + 2 shows
an imitative motion (the caregiver observes the infant’s
right hand movement in time step t + 1 and shows same
motion in time step t + 2). To the contrary, the caregiverin time step t + 1 does not show an imitative motion, i.e.,

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performs a randomly selected motion (the infant’s motion
in time step t is left hand movement but the caregiver’s
motin in time step t + 1 is right hand movement).
• The caregiver has a perfect body mapping, while theinfant does not know the correct correspondence and does
not distinguish between observed self and other motions.
The infant imitates by executing a body motion whichcorresponds to the observed body motion according tohis/her immature body mapping.
• The infant learns the body mapping using unsupervised
learning, that is, without any explicit reward.
The body mapping is learned simply by associating motor
commands with observed motions.
• The agent can predict the successive observation fromthe self motor command by using the body mapping
inversely.
The body mapping is represented by a network as shown in
Fig.2. An observed body motion is represented by one nodein the visual representation layer and the motor commands
for a body motion are represented by a single node in the
motor representation layer. For the sake of convenience, theobserved self-motions are displayed in the left half of thevisual representation layer and the observed other’s motions

are displayed in the right half, though the learning rules do
not discriminate between the sources of the body motions.
In the motor representation layer, two nodes indicate thesame motion command by which the infant can acquire two
mappings: a mapping that associates an observed self-motion
with the corresponding self-motor command (self-model) anda mapping that associates an observed other’s motion with thecorresponding self-motor command (other-model). When theagent imitates the observed motion, it is done by executing
a body motion which corresponds to the observed motion
according to the agent’s body mapping.
Initially, the infant’s connections of the mapping are immature (i.e., connected with small random weights as shownin Fig.3). A Hebbian learning rule reinforces associations between the self-motor commands with the corresponding body
motion observed at the same time that the motor command is
executed. The caregiver has a perfect body mapping in which
the self-model and other-model are correctly separated andboth layers are correctly connected (Fig.3)). The infant acquires the body mapping if he/she associates the correct motor
commands with the observed caregiver’s imitative motions.
The self-other distinction is essentially a problem to discriminate sensory information that always synchronizes withthe self-motion from the other sensory information. This
problem occurs when there are some moving objects in theenvironment around the infant, one of which is the caregiver.
Caregivers actually does not always act at the same time that
infants move, however, we assume the caregiver and the infant
always move at the same time as a simple setting to deal withthe self-other distinction problem. In order to discriminate
between observed self generated motions and those of theother, the self-model and the other-model need to be represented separately. One of the clues needed by the infant inorder to acquire these separate models is a difference in the
delay of observation. When a motor command is executed, thecorresponding self generated motion is observed immediately,while the corresponding other’s motion is observed with a one
step delay (assuming that the other is imitating). In order tomake use of the difference in the delay of observation, thebody mapping model is assumed to have a structure in which
the motor command is copied back to the motor representation
layer in two ways: without delay and with a one step delay.
These are equivalent to a proprioceptive feedback of a motor
command and a memory of the proprioceptive feedback. For
the sake of convenience, motion commands copied without
delay are called the self-related motions (left part of the motor
representation layer in Fig.2), and motion commands copiedwith a one step delay are called the other-related motions (rightpart).
The simulation proceeds as follows: (a) both agents executea motor command, (b) the infant updates the body mapping,(c) both agents select a new motion to perform, as shown in
Fig.4, and this process is repeated.
(a) The current motor command and the previous motor
command are copied to the motor representation layer(Ms , Mo ) when the motor command is executed. The

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resulting observations are predicted (Vs , Vo ) from Ms
and Mo with the inverse mapping of the body mapping.
(b) The body mapping is updated by strengthening the connection weights between the observed motions (V ) andthe copied motor commands on the motor representation
layer (Ms , Mo ) using a modified Hebbian learning rule
which takes mutual exclusivity into consideration [17].
(c) The motions corresponding to the observed motions
are found by the body mapping (Ms , Mo ), and theprediction errors (Es , Eo ) are calculated from V , Vs ,and Vo . The next motion is chosen between Ms andMo based on the prediction errors.
Since the agent observes two motions (self-motion andother’s motion) at the same time, two motions (self-related
motion and other-related motion) are retrieved from the observed motions as shown in Fig.4 (c). When the agent imitates
the observed motions he/she must choose an imitative motion
from two motions. The self-related motion means imitating
self-motion (self-imitation) and the other-related motion means
imitating the other’s motion. We hypothesize that the agent
chooses the motion based on the predictability of the observation. This paper proposes a predictability preference for motion
decision, which is a function relating predictability to action
selection. The agent predicts the resulting observations fromthe activations in the motor representation layer by inverting
the body mapping (the self-model and other-model are notdiscriminated). Two patterns of the observation (Vs , Vo ) are
predicted from the copied current motor command Ms andprevious motor command Mo as shown in Fig.4 (a). Whenthe agent observes the motions, two prediction errors (Es , Eo )are calculated, which are related to Ms and Mo , respectively.
The preferences for the self-related and other-related motions(Ps , Po ∈ [0, 1]) are determined based on the prediction errors
Es and Eo , respectively. The preference curve modulates thePreference

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preference of a motion based on the prediction error, as shownin Fig.5. The preference is assumed to be determined not onlyby the current prediction error but also the prediction errors
in the past several steps; here the averaged prediction errors(Ēs , Ēo ∈ [0, 1]) are used. In addition, the agent can choosea random motion (Mr ) as an additional option as well as
imitative motions. The preference for the random motion isdefined as Pr = 1 − max(Ps , Po ) so that Pr has a high value
when both the preferences for imitative motions have low
values. The agent probabilistically chooses a motion among
Ms , Mo , and Mr in proportion to the ratio of Ps , Po , and Pr .
If the body mapping is correct, the self-motion is correctlypredicted from Ms . The other’s motion is correctly predictedfrom Mo only when the other imitates. The agent’s action
selection affects the other’s prediction error, and therefore
determines the balance between self-imitation, imitating other,and randomly selected motion, which in turn affects the courseof the interaction and the development of imitation.
III. S IMULATIONS
A. Simulation settings
In order for the infant to acquire the body mapping andimitation capability, he/she needs to elicit the right balanceof imitative motions from the caregiver. Too much imitationfrom the caregiver might make it difficult for the infant to1
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number of predicted motions. The averaged predicted errors(Ēs ,Ēo ) are calculated from the errors in the last 20 steps.

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Test patterns of preference curve.

discriminate their own motions from those of the caregiver,whereas too little imitation will not allow the infant to fully
develop a correct mapping for self and other motions. In our
simulation, the preference curve influences this balance ofimitation. We hypothesize that a typical, healthy preference
leads to a typical developmental process and an atypicalpreference can only result in a disordered body mapping.
We investigated the effects of using different shaped preference curves on the developmental process of the bodymapping. We tested eight distinct preference curves for the
infant. The profiles of the curves are qualitatively different,
as shown in Fig.6. We set the range of preference values
to [0.1, 0.9] so as to avoid extreme cases (e.g., the agent
always preferring the self-related motions). The prediction
error essentially indicates a measure of novelty in the resultant
observation. The meanings of the preference curves are:
A Nothing: Mostly choose random behavior.
B Everything: Mostly try to imitate.
C Comfort zone: Prefer neither too much familiarity, nor
too much novelty
D Extremes: Prefer very familiar or very novel situations
E Novelty avoiding: Dislike very novel situations
F Familiarity avoiding: Dislike very familiar situations
G Novelty greedy: Prefer very novel situations
H Familiarity greedy: Prefer very familiar situations
Preference curve (C) simulates Wundt curve where greatest
pleasure comes from a moderate amount of stimulus novelty,
which is considered to be a person’s intrinsic preference [18].
It shows a characteristic that the agent does not prefer motions
from which successive results can be accurately predicted (i.e.,
results are too-familiar) and cannot be completely predicted(i.e., results are too-novel). This curve shows a inverted-U
relationship between novelty (opposite of familiarity) and preference. Many studies have shown that this kind of relationshipappears in psychological experiments [19, 20]. The caregiver
was assumed to be a typical healthy person, and was therefore
given this preference curve.
The simulation assumes that both agents have 30 patternsof body motion. In the simulation, a motion pattern is coded
as a symbol and the agents interaction is implemented insymbol communication. The range of the connection weightsof the body mapping is [0, 1], and the infant’s initial weights
are set randomly in the range of [0, 0.1]. The caregiver has
a value of 1.0 on the correct connections and 0.0 on thewrong connections. In the prediction phase, we assume that

B. Results
The averaged results of 20 trials are shown in Fig.7. One
trial is terminated at 10000 time steps. The caregiver always
uses preference curve (C), and each column of the figure shows
the graphs when the infant is using curves (A)-(H). Each row
in the figure shows the following results:(1) Ratio of wrong connections in the infant’s mapping.
The graph shows ratios of the number of motions which
are not correctly connected in the infant’s self-modeland other-model. The abscissa shows the simulation time
step [0, 10000] (the same for each row). Here, we count acorrect connection as follows: when a connection froma node in the visual representation layer has maximal
weight among the connections from the node, it iscorrectly connected to the corresponding node in the
motor representation layer, and the difference between
its weight and the second maximal weight is more than athreshold (0.5), we count it as a correct connection. The
threshold is used to check exclusivity of the connection.
(2) Rate of selected motion in the infant’s action selection.
The graph shows rates of the number of times the selfrelated motion Ms , the other-related motion Mo , and therandom motion Mr are selected in the last 20 steps.
(3) Rate of selected motion in the caregiver’s action selection. The same as (2) for the caregiver.
(4) Acquired mapping of the infant.
The network shows the qualitative features of the mapping acquired by the infant. Solid lines means that over
80% of the correctly corresponding connections havestrong weight (more than 0.5), dashed lines means that
20% to 80% have a strong weight, and with less thanthat no lines are drawn.
In our simulation results, only infants with preference curve(C) can successfully acquire the correct body mapping inwhich the self-model and other-model are clearly separated, as
can be seen in Fig.7 (4). When the infant has preference curves(B), (D), (E), or (F), the observed motions are correctly associated with the self-motor commands but the self-motions andother’s motions are not distinguishable. When the infant has
preference curves (A), (G) or (H), the observed self-motions
are correctly associated with the self-motor commands but
some observed other’s motions are not associated with any
motor commands (the weights are not zero but are too small to
be considered exclusive). This means that the infant is unable
to construct a model of the other.
a) Typical developmental process: The infant using preference (C) frequently chooses self-related motions for the first
300 steps but then the frequency quickly decreases as can be

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seen in the left of Fig.8. Then, the frequency of the otherrelated motions increases relative to the self-related motions,and the infant acquires the other-model. This indicates a developmental process in which the infant’s self-imitation appears
early on, and disappears once the self-model is acquired. Thenthe mutual imitation between the infant and the caregiver
begins. The resultant processes, therefore, involve the processof transition from self to mutual imitation, that is, the early
developmental process of imitation.
The self-imitation in the results is quickly inhibited. It
is inferred that the infant confuses the self-model and theother-model if he/she continues to self-imitate. It can be also
said that the self-model and the other-model are confused
if the caregiver keeps repeating the same imitative motion.
We can see from the graph on the right of Fig.8 that the
caregiver in these results frequently shows random motions,which work as switching motions. This is due to the low
preference for motions from which the agent can accurately
predict a successive observation (i.e., motions which elicit toofamiliar motions), and this characteristic could be necessary
for a typical development.
b) Atypical developmental process: In the results withpreferences (B), (D), (E), and (F), it was observed that the
infant chooses random motions with low frequency, as canbe seen in Fig.7 (2) and tends to keep same motions. The

caregiver is encouraged to imitate these actions, then thisresults in an infant who has trouble differentiating the observed
actions. This is because the infant has high preference for awide range of the prediction error. Meanwhile, when the infant
has preferences curve (A), (G), or (H), the caregiver does notoften imitate (the rate of selected other-related motion is low in
Fig.7 (3)) and the infant, therefore, cannot acquire the othermodel. These infants could not elicit the imitation behavior
from the caregiver because:• The infant (A) always prefers random motions.
• The infant (H) prefers only self-imitation due to thequickly acquired self-model.
• The infant (G) prefers using the immature other-model
rather than the mature self-model.
Since the caregiver is assumed to have preference curve (C),
it is up to the infant to choose behaviors that are within thelimits of acceptable predictability. The infant must be able
to elicit well-balanced imitation behavior from the caregiver.
Otherwise, it is incapable of forming the correct mapping.
It is considered that the confused body mapping and thedeletion of the other-model express developmental disorders;the former indicates a disorder in self-other distinction andthe latter indicates a disorder in understanding other people.
For example, earlier psychoanalytic theories have suggested
that a developmental disorder of distinction between self andnon-self is fundamental to children with autistic spectrum
disorders (ASD) [21]. A confused body mapping could be
related to these failures in self-other distinction. Furthermore,
psychological studies have reported that children with ASD
lack a theory of mind [22]. A body mapping without another-model could be related to the failure in estimating otherpeople’s internal states.
Concerning the preferences, it has been observed that developmentally disordered children tend to show strong interest in
one object and repeat the same behavior patterns (especiallychildren with ASD [23]), and that this tendency could be
related to the preferences (B), (D), (E), and (F). It has also beenobserved that developmentally disordered children tend not toinitiate communication with other people (especially children
with ASD [23]), and this tendency could be also related to
low preference for the wide range of the prediction error in
preferences (A), (G), and (H). The preference curve (H) isfor highly-predictable motions but the agents do not initiate
communication because they prefer only self-imitation. The
infant with preference curve (G) prefers using the immatureother-model (i.e., always explores new things) and, therefore,
does not communicate with other people.
These results suggest that a failure in acquisition of ahealthy body mapping for imitation stems from atypical preferences of individuals, though it is necessary to investigate
why the atypical preferences occur in the first place.
C. Summary
From the results shown above, it is considered that typicaldevelopment (the shift from self to mutual imitation) requires
the preference to neither too much familiarity nor too muchnovelty in order to avoid the perseverance of certain motions
and to elicit various imitation from the caregiver. The preference with the inverted-U shape, which is typical in a healthy
person, leads to a typical developmental process while theatypical preferences leads to a disordered body mapping. We
emphasize that a typical developmental process of transition
from self to mutual imitation emerged from our system without
any explicit mechanism of developmental order. The results
suggest that the predictability preference is a very importantfactor in the development of an infant’s body mapping, whichenables it to distinguish self-motion from other’s motion andgives it the ability to imitate both.
IV. C ONCLUSION
In order to study the mechanisms of early imitation development, a model was made that was able to develop ahealthy body mapping, which can discriminate self-motion
from the other’s motion, during the interaction between infant
and caregiver in an imitation game. Although the model is
not based on anatomical evidence of biological systems, we
assume that humans have something equivalent to our system,with mechanisms to utilize the difference in observational
delay and to choose self-imitation and other-imitation in orderto solve problems of self-other distinction and body mapping
acquisition from mutual imitation. It has been shown thattypical developmental process of transition from self to mutual
imitation can emerge from our system without any explicit
mechanism of developmental sequence. We also have shown
the inverted-U preference curve is indeed a viable proposal for
healthy development. The analysis of the simulation results isstill speculative but suggests that the predictability preferenceis one of the factors which govern the early developmental
process of imitation capabilities. Future work will need tojustify the model and the resultant developmental process bycomparing them with human infants’ natural developmental
processes.

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